本文關鍵詞：跳擴散框架下股票交易策略及二叉樹模型研究　出處：《揚州大學》2012年碩士論文　論文類型：學位論文

  更多相關文章： 跳擴散模型 Black-Scholes市場 最優(yōu)停時問題 效用函數(shù) 回望期權 二叉樹方法 收斂性

【摘要】：本文研究當市場中資產的價格服從跳擴散模型時的股票交易策略及二叉樹模型的問題。與傳統(tǒng)擴散模型不同,跳擴散模型假設資產的價格過程同時受到布朗運動和泊松過程的控制,它可以較好的解釋由于突發(fā)事件(如末期財政數(shù)字的公布、重大事件以及自然災害等)所導致的市場價格的劇烈變化,故比擴散模型更加合理的描述了市場的運作規(guī)律。 如果股票持有者必須在一段給定的時間賣出股票,何時是最佳的賣出時間?當然每個投資者都希望在這個時間段內股票達到它的最大值時賣出股票,但是這是不可能實現(xiàn)的。本文利用最優(yōu)停時理論研究了使股票賣價相對于股價在整個時間段內整體最大值在某些效用函數(shù)作用下達到最大時的交易策略。在假設股票價格服從跳擴散模型的框架下,當效用函數(shù)取對數(shù)函數(shù)和線性函數(shù)時,本文給出了判斷股票“好壞”的標準,驗證了最佳的交易策略是對“好的”股票應該長期持有直到最后期限時賣出,而對“壞的”則應立即拋出。 二叉樹方法是期權定價的最重要的數(shù)值方法之一,Kim等人[1]研究了在跳擴散模型下的回望期權定價的二叉樹方法,但是他們提出的二叉樹方法與對應連續(xù)模型是不相容的。我們從PDE的方法出發(fā)提出了一種相容的修正的二叉樹方法,并研究它的自由邊界的收斂性及二叉樹模型下的美式期權的相關性質。
[Abstract]:This paper studies the strategy of stock trading price when the market asset follows a jump diffusion model and the two fork tree model. Different from the traditional diffusion model, jump diffusion model assumes that the asset price process and controlled by Brown and Poisson process, it can better explain the unexpected events (such as the end of published financial figures the major events and natural disasters) caused drastic changes in the market price, so it is more reasonable than the diffusion model the operation of the market.
If the stock holders must sell the stock in a given period of time, when is the best time to sell? Of course, each investor hopes to share in this period of time it is the maximum value of selling the stock, but this is not possible. In this paper, using the optimal theory of the stock price relative to the overall price in the whole time the maximum period reaches the maximum value when the trading strategy in some utility function to stop. The framework follows a jump diffusion model under the assumption that the stock price, when the utility function of the logarithm function and linear function, this paper gives the judge the stock "quality" standard, to verify the optimal trading strategy is to sell until the deadline hold on "good" stock should be, and the "bad" should be immediately thrown out.
Two binary tree method is one of the most important numerical methods for option pricing, Kim et al [1] studied two binary tree method in jump diffusion model of the pricing of lookback options, but with the corresponding two tree method of their continuous model is incompatible. We start from the PDE method proposed two binary tree a method of compatibility correction, related properties of American option and convergence of two binary tree and investigate the free boundary model.

【學位授予單位】：揚州大學
【學位級別】：碩士
【學位授予年份】：2012
【分類號】：F830.91;F224

【參考文獻】

相關期刊論文 前1條

1 戴民;NUMERICAL ANALYSIS ON BINOMIAL TREE METHODS FOR AMERICAN LOOKBACK OPTIONS[J];Numerical Mathematics A Journal of Chinese Universities(English Series);2001年02期

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本文編號：1387142